Extreme multistability in memristive hyper-jerk system and stability mechanism analysis using dimensionality reduction model

Abstract

This paper presents a memristive hyper-jerk system with smooth hyperbolic tangent memductance nonlinearity. Such a smooth memductance nonlinearity can cause the system to possess a line equilibrium therein, leading to the emergence of extreme multistability with coexisting infinitely many attractors due to the existence of a zero eigenvalue. To illustrate the stability mechanism, the dimensionality reduction model of the memristive hyper-jerk system is obtained using state variable mapping (SVM) method and several isolated equilibria are yielded from the dimensionality reduction model. As a consequence, the initial-dependent extreme multistability in the memristive hyper-jerk system is converted into the initial-related parameter-dependent dynamics in the dimensionality reduction model and the stability mechanism analysis is thereby executed. Furthermore, PSIM circuit simulations based on a physical circuit are performed to confirm the coexisting infinitely many attractors.